CLEVELAND — Sen. Mike Lee of Utah is being tight-lipped about whether he plans to support a last-ditch effort to steer the nomination away from Donald Trump at the Republican National Convention.

Mr. Lee is arguably the most high-profile member of the 112-member rules committee that is set to take up a “conscience clause” amendment here Thursday or Friday that would unbind delegates from being forced to support Mr. Trump, freeing them up to support someone else.

“We’ll see,” Mr. Lee told The Washington Times Thursday on his way into a convention rules committee meeting. Asked whether he has made up his mind, Mr. Lee said, “I have a pretty good idea, and I look forward to it.”

The effort to derail Mr. Trump through a rules change is being led by Kendal Unruh, a conservative activist from Colorado.

Ms. Unruh’s amendment is not expected to pass the committee, but she claims to have the support of 28 members of the committee — enough to adopt a so-called “minority” report, thereby keeping the effort alive and giving the entire convention the chance to weigh in on the issue.

Winning over Mr. Lee, who has been critical of Mr. Trump, could give the effort some star power and likely a boost.

Ed Martin, president of the Eagle Forum, said the stakes are high for people like Mr. Lee and Sen. Ted Cruz of Texas, both of whom have refused to endorse Mr. Trump.

“These guys have to decide if they are George Romney or Richard Nixon in 1964,” Mr. Martin said, suggesting they should fall in line and support Mr. Trump.

“George Romney refused to help the nominee and faded away. Nixon worked his tail off for Goldwater and by ‘68, he was the nominee,” he said.